# Particle moving in a one-dimensional potential

• Identify
In summary, the conversation discusses a one-dimensional potential and its corresponding wavefunction at time t=0. The probability distribution for the particle's position at this time is given by |Psi(x,0)|^2. The conversation also touches on the nature of a wavefunction and its relation to periodicity.
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## Homework Statement

A particle moving in a one-dimensional potential is in a state such that its wavefunction at time t=0 is:

Psi(x,0)=A(x-a)x, 0<=x<=a, and
Psi(x,0)=0, otherwise.

Sketch |Psi(x,0)|^2, which gives the probability distribution describing the position of the particle at time t=0.

As above

## The Attempt at a Solution

I am thrown by Psi in this question. It doesn't even resemble a wavefunction. Am I simply supposed to square the absolute value of the polynomial?

Yes. Why do you say it "doesn't even resemble a wavefunction"?

Because its not a periodic function.

Why should it be periodic? Are sure what is meant by a "waveform" here?

Shouldn't a wavefunction resemble a wave? ie be periodic?

You are confusing a wavefunction with a periodic function such as a sinusoid of varying harmoics, etc. The wavefunction is essentially a probability amplitude for (in this case) the location of a particle.

It is, (in this case) a one dimensional wave and you can model its motion using a (rather famous) relation that looks quite close to the wave equation, shown here:

[ tex ] \nabla^2 f(x,y,z) = \frac{1}{c^2} \frac{\partial f(x,y,z)}{\partial t} [ /tex ]

Last edited:
Identify said:
Shouldn't a wavefunction resemble a wave? ie be periodic?
Nope. A pulse traveling down a string, for instance, is a wave. There's no requirement for periodicity at all.

by the way...why isn't my tex being formatted?

## What is a one-dimensional potential?

A one-dimensional potential is a simplified model used in physics to describe the motion of a particle along a single axis. It is typically represented as a function of the particle's position, and can be used to calculate the particle's potential energy and forces.

## How does a particle move in a one-dimensional potential?

A particle moving in a one-dimensional potential will experience a force that is proportional to the negative gradient of the potential function. This force will cause the particle to accelerate in the direction of decreasing potential energy, until it reaches a state of equilibrium where the net force is zero.

## What is the difference between a one-dimensional potential and a three-dimensional potential?

A one-dimensional potential only considers motion along a single axis, while a three-dimensional potential takes into account motion along three axes (x, y, and z). This means that a three-dimensional potential is a more complex model and can better describe the motion of particles in three-dimensional space.

## How is the potential energy of a particle related to its position in a one-dimensional potential?

The potential energy of a particle in a one-dimensional potential is determined by the value of the potential function at its position. A higher potential energy corresponds to a higher value of the potential function, while a lower potential energy corresponds to a lower value of the potential function.

## What is the significance of equilibrium points in a one-dimensional potential?

Equilibrium points in a one-dimensional potential represent positions where the net force on the particle is zero and the particle is at rest. These points can also correspond to minimum or maximum potential energy values, as well as points of stable or unstable equilibrium depending on the shape of the potential function.

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